A jet of water impinges on a series of curved vanes at an angle of 30° to the direction of motion of the vanes while entering and leaves the vanes horizontally. The head under which the jet issues from the nozzle is 30 m, the coefficient of velocity for the nozzle is 0·9 and the diameter of the jet after leaving the nozzle is 50 mm. The speed of the vanes is 10 m/s and the relative velocity of the water at outlet is 0·8 times the relative velocity at inlet. Calculate : (i) The angle of vane tips at inlet; (ii) The power developed by the jet, and (iii) The efficiency of the system.
Answers
Answer:
a jet
Explanation:
t of water of diameter 5cm moving with a velocity of 25 m/sec impinges on a
fixed curved plate tangentially at one end at an angle of 30˚ with the horizontal.
Determine force of the jet on the plate in the horizontal and the vertical direction if
the jet is deflected through an angle of 130˚. Also find direction and resultant force.
[Ans: 2216.06N, 193.88N, 2224.5N, 4.99˚] [14; V. L. Patel]
2. A jet of water impinges on a symmetrically curved vane at its center. The velocity of
the jet is 60 m/s and the diameter 120 mm. The jet is deflected through an angle of
120°. Calculate the force on the vane if the vane is fixed. Also determine the force if
the vane moves with a velocity of 25 m/s in the direction of the jet. What will be the
power and efficiency? [GTU; DEC – 2010]
3. A jet of water having a velocity of 20 m/sec strikes a curved vane, which is moving
with a velocity of 10 m/sec. The jet makes an angle of 20˚ with the direction of
motion of vane at inlet and leaves at an angle of 130˚ to the direction of motion of
vane at outlet. Calculate:
(1) Vane angles, so that the water enters and leaves the vane without shock.
(2) Work done per unit weight of water striking the vane per second.
[Ans: 37.876°, 6.565°, 20.24 N-m/N] [17.18; R. K. Bansal]
4. A jet of water having a velocity of 15 m/sec strikes a curved vane which is moving
with a velocity of 5 m/sec. The vane is symmetrical and it so shaped that the jet is
deflected through 120˚. Find the angle of the jet at inlet of the vane so that there is
no shock. What is the absolute velocity of the jet at outlet in magnitude and direction
and the work done per unit weight of water? Assume the vane to be smooth.
[Ans: 20.405°, 6.62m/s, 127.83°, 9.225 N-m/N] [17.21; R. K. Bansal]
5. A jet of water having a velocity of 15 m/sec, strikes a curved vane which is moving
with a velocity of 5 m/sec in the same direction as that of the jet at inlet. The vane is
so shaped that the jet is deflected through 135˚. The diameter of jet is 100mm.
Assume the vane to be smooth, find:
(1) Force exerted by the jet on the vane in the direction of motion.
(2) Power exerted on the vane.
(3) Efficiency of the vane [Ans: 1340.6N, 6.703KW, 50.5%] [17.23; R. K. Bansal]
6. A jet of water of diameter 5 cm having a velocity of 30 m/sec strikes a curved vane
horizontally at one of its tip which is moving with a velocity of 15 m/sec in the
direction of jet. The jet leaves the vane at an angle of 60˚ to the direction of motion of
the vane at outlet. Determine :
(1) The force exerted by the jet on the vane in the direction of motion
(2) The work done per second by jet. [Ans: 662.68N, 9.94KW] [21; V. L. Patel]
7. A jet of water having a velocity 25 m/s strikes on a series of vanes moving with a
velocity 10 m/s. The jet makes an angle of 300 with the direction of motion of vanes
when entering and leaves at an angle of 1500 with the direction of motion. Sketch
the velocity triangles and calculate,
(i) The angle of vane tips at the inlet is 50.8°.
(ii) The power developed by the jet is 8.652 kW.
(iii) The efficiency of the system is 71.2 %.
Given: The Angle of the curved vanes = 30°,
The head available at nozzle = 30m
The coefficient of velocity for the nozzle is 0·9, and the diameter of the jet after leaving the nozzle is 50 mm.
The speed of the vanes is 10 m/s and the relative velocity of the water at the outlet is 0·8 times the relative velocity at the inlet.
To Find:
(i) The angle of vane tips at the inlet;
(ii) The power developed by the jet, and
(iii) The efficiency of the system.
Solution:
(i) We are required to find the angle of vane tips at the inlet ( α ) ;
We are given that,
Coefficient of velocity (Cv) for the nozzle = 0·9,
The head (H) available at nozzle = 30m
We know that, V1 = Cv × √(2gH)
= 0.9 × √(2 × 9.8 × 30)
= 21.034 m/s
From the inlet velocity triangle given in the diagram,
V1 cos 30° = Vr1 cos α + 10 [ where speed of the vanes (u1) = 10 m/s ]
⇒ Vr1 cos α = V1 cos 30° - 10
⇒ Vr1 cos α = 21.034 × √3/2 - 10
⇒ Vr1 cos α ≅ 8.91 m/s ....(1)
Again, V1 sin 30° = Vr1 sin α
⇒ Vr1 sin α = 21.034 × 1/2
⇒ Vr1 sin α ≅ 10.92 m/s ....(2)
Now, dividing (2) by (1), we get;
Vr1 sin α / Vr1 cos α = 10.92 / 8.91
⇒ tan α = 1.225
⇒ α = 50.78°
= 50.8°
Hence, the angle of vane tips at the inlet is 50.8°.
(ii) Now, we are required to find the power developed by the jet,
Putting the value of α in (1), we get;
Vr1 cos 50.8° = 8.91
⇒ Vr1 = 14.09 m/s
Now, we are given the relative velocity of the water (Cb) at outlet = 0·8
So, Vr2 = Cb × Vr1
= 0.8 × 14.09
= 11.27 m/s
From the outlet velocity triangle, u2 = 10.
Vw2 = Vr2 - u2 = 11.27 - 10 m/s
= 1.27 m/s
Vw1 = V1 cos 30° = 21.034 × 1/2
= 10.91 m/s
For calculating the Power, we shall make use of the formula,
P = m × ( Vw1 + Vw2 ) × u1 .....(3)
where m = eAV1
⇒ m = 1000 × π/4 × (0.050)² × 21.034
= 42.072 kg/s
Putting the value of m in (3), we get;
P = m × ( Vw1 + Vw2 )
⇒ P = 42.072 × ( 10.91 + 1.27 ) × 10
= 42.072 × 12.18 × 10
= 8652.99 W
≅ 8.652 kW
Hence, the power developed by the jet is 8.652 kW.
(iii) For calculating the efficiency of the system, we need to find the total power available to the nozzle, which is given by the formula,
Total power available = egAH
= 1000 × 9.8 × π/4 × (0.050)² × 21.034 × 30
= 12136.09 W
Power developed = 8652.99 W
Now, we know that efficiency can be calculated by the formula,
Efficiency = Power developed / Total power available
= 8652.99 / 12136.09
= 0.712
Efficiency % = 0.712 × 100
= 71.2 %
Hence, the efficiency of the system is 71.2 %.
Compiling all the answers, we get;
(i) The angle of vane tips at the inlet is 50.8°.
(ii) The power developed by the jet is 8.652 kW.
(iii) The efficiency of the system is 71.2 %.
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